Opinions differ. It is easy to find "authoritative" sources arguing for either view, and one is often treated to collections of quotations aimed at establishing the inclusion of mathematics within science.

It should come down to what the current conception of science may reasonably be said to encompass. If you see current science as an exploration of the natural world premised upon accepting or rejecting concepts based upon their consilience with the physical evidence, then you would also see math as an often-useful tool, but not a sub-field of scientific endeavor. The field of mathematics as a whole is premised upon operations performed within a logical framework, and only within applied sub-fields is there any need to check for fit between the math and empirical evidence.

If one expands the definition of science as "intelligent design" creationism (IDC) advocates have attempted many times to do, as a way of proposing logically consistent explanations for phenomena only and with no necessity to measure up to the test of the evidence, then you will see IDC included within science, as well as astrology, and mathematics, too. For the IDC advocates, then, mathematics must be science if their own bizarre views have any hope to be so-called. One can see that the trenchant and forceful way that IDC advocates insist upon math in general being science is simply part of looking after their own self-interests.

My opinion:As a field, it seems to me that mathematics has sufficient honor that it little needs to borrow such that may be found by artificially terming it to be science. Certainly one should discount the socio-political push coming from pseudo-scientists as a reason for including math within science.

I would say something here, but somebody already pointed out that science depends on conclusions being consistent with physical properties of the thing under study. Conclusions in math don't depend on that even when a physical system is being used to model the math system.

But since somebody already made that point, I won't bother repeating it.